Income distribution dependence of poverty measure:a theoretical analysis

Chattopadhyay, Amit K. and Mallick, Sushanta K. (2007). Income distribution dependence of poverty measure:a theoretical analysis. Physica A, 377 (1), pp. 241-252.

Abstract

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the 'global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy. © 2006 Elsevier B.V. All rights reserved.

Publication DOI: https://doi.org/10.1016/j.physa.2006.10.103
Divisions: Engineering & Applied Sciences > Mathematics
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Physica A. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Chattopadhyay, AK & Mallick, SK, 'Income distribution dependence of poverty measure: a theoretical analysis' Physica A, vol. 377, no. 1 (2007) DOI http://dx.doi.org/10.1016/j.physa.2006.10.103
Uncontrolled Keywords: consumption deprivation,income distribution,inequality,inflexion point,poverty,correlation methods,data reduction,developing countries,function evaluation,social aspects,surveying,developing economy,cost accounting
Published Date: 2007-04

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